Didem Akyuz

Improving the Quality of Mathematics Teaching with Effective Planning Practices.

Although it has been two decades since National Council of Teachers of Mathematics Standards were published, research underlines the lack of essential practices for quality reform teaching. The literature also emphasizes the importance of planning in reform teaching although few studies focus directly on the planning of the teacher. This study attempts to shed light on teacher planning through a particularistic case study within a design research experiment which was performed to improve the quality of teaching. In particular, this study aims to extract the planning practices of an expert seventh-grade mathematics teacher before and during instruction on integers. The extracted practices were interpreted through the teaching-in-context theory, which uses beliefs, goals, and knowledge as the backbone of the analysis. The results indicate that five core practices underlay the development of effective planning: preparation, reflection, anticipation, assessment, and revision. Each practice included multiple actions performed in an environment of collaboration.

Çember Özelliklerini Öğretmeyi Amaçlayan Teknoloji ve Sorgulama Tabanlı bir Sınıfta Oluşan Sosyomatematiksel Normların İncelenmesi

This article aims to document the discovery of sociomathematical norms by prospective teachers in a technology and inquiry based classroom, and the role played by the instructor in this process. The findings are obtained from the dialogs between the prospective teachers and the researcher as well as from classroom communications observed during a 5-week long instructional period that was focused on teaching circle properties. After the transcription of these communications, the repeating patterns of explanations, interpretations, proofs, and argumentations are extracted which are then classified as sociomathematical norms based on the existing theoretical frameworks. Special emphasis was put on three norms that relate to using technology. These norms were (1) inquiring about the effects of a change made in a question or a solution; (2) reaching conclusions by using the properties of the tools in the dynamic software; and (3) dynamically verifying a solution or a hypothesis. It is hoped that the findings of this study can help other researchers, teachers, teacher candidates, and instructors that educate teacher candidates who desire to create inquiry based teaching and learning communities that have established sociomathematical norms.

Teaching Integers to Students with Disabilities: Three Case Studies

The main purpose of this chapter is to document the reasoning of three students, two with disabilities and one with mathematical difficulties, as they participated in and contributed to the classroom mathematical practices established by a seventh-grade class during integer instruction. The integer instructional sequence was designed to support students’ increasingly sophisticated reasoning about integers and meaning making for integer addition and subtraction. This chapter builds on our prior work that identified the classroom mathematical practices established by the teacher and students during implementation of the integer sequence (Stephan M, Akyuz D, J Res Math Edu 43:428–464, 2012). In particular, because the integer sequence was implemented in an inclusive setting, we have the unique opportunity to document the learning of two students with disabilities and one with difficulties as they participated in an inquiry environment, contributing to the development of the classroom mathematical practices. These three students participated in a classroom teaching experiment held in a co-taught classroom in which students with disabilities were included with regular education students. Therefore, the three case studies we present illustrate a rare analysis of the integer learning of students with disabilities. The primary research question that we seek to answer through this chapter is, how do students with learning disabilities make meaningful contributions to the development of classroom mathematical practices and gain intellectual autonomy in the process of learning integer concepts and operations?

Measuring technological pedagogical content knowledge (TPACK) through performance assessment

Abstract Despite many studies conducted on TPACK, the relationships between the components of the framework and how to perform TPACK assessment remain to be important research questions. The aim of this study is to shed light on these two questions by analyzing lesson plans collected from 138 preservice mathematics teachers obtained from a technology-integration course over a period of five years. An instrument that describes each component of the TPACK framework was developed and applied to performance-assessment of preservice teachers. The analysis is augmented by a self-assessment survey to compare and contrast the differences between the two. According to the results, four knowledge domains within the TPACK framework could be distinguished, which are denoted as Core, Tech, TPACK-P, and TPACK-C. The performance- and self-assessment based measures were found to yield similar results except for pedagogy related knowledge domains, in particular for pedagogical knowledge (PK), technological pedagogical knowledge (TPK), and the TPACK.